Undergraduate Course: Honours Differential Equations (MATH10066)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 10 (Year 3 Undergraduate) 
Availability  Available to all students 
SCQF Credits  20 
ECTS Credits  10 
Summary  Core course for Honours Degrees involving Mathematics.
This is a second course on differential equations discussing higher order linear equations, Laplace transforms, systems of First Order Linear ODEs, nonlinear systems of ODEs, Fourier Series, use of separation of variables in standard PDEs and SturmLiouville Theory.
In the skills section of the course, we will work on symbolic manipulation, computer algebra, graphics and a final project. Platform: Python in computer labs. 
Course description 
Syllabus : Systems of First Order Linear ODEs with constant coefficients using linear andmatrix algebra methods.
Numerical methods: Euler, Heun, RK
Nonlinear systems of ODEs: critical points, linear approximation around a critical point; introduction to nonlinear methods: Lyapunov functions.
Fourier series
PDEs by separation of variables
SturmLiouville theory
Laplace transform
Skills : Python brush up: functions, plotting.
Systems of 1st order ODEs: plotting phase portraits, using SciPy ODE solvers.
Nonlinear systems: exploring dynamical systems (limit cycles, chaos in the Lorenz model, in the periodically perturbed pendulum...) using SciPy ODEsolvers.
Numerical methods for ODEs: implementing Euler, Heun, etc.
Fourier: comparison function/truncated series, perhaps computation of Fourier coefficients.
PDEs: plots of 2D functions, animations.

Information for Visiting Students
Prerequisites  Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2023/24, Available to all students (SV1)

Quota: None 
Course Start 
Semester 1 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
200
(
Lecture Hours 35,
Seminar/Tutorial Hours 10,
Supervised Practical/Workshop/Studio Hours 10,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
138 )

Assessment (Further Info) 
Written Exam
70 %,
Coursework
30 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 30%, Examination 70%

Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)   3:00  
Learning Outcomes
On completion of this course, the student will be able to:
 Solve systems of linear ordinary differential equations, selecting the most appropriate method, including Laplace transform.
 Describe the behaviour of solutions of systems of nonlinear ordinary differential equations, locally by identifying critical points and determining their nature, and globally by identifying periodic orbits.
 Apply the method of separation of variables to solve simple linear PDEs (heat, wave and Laplace equations and similar), and demonstrate understanding of the SturmLiouville theory underpinning the method.
 Use appropriate symbolic and numerical methods in Python to solve and analyse differential equations.
 Carry out a small individual investigation, making use of Python, and produce a written report on the outcomes.

Reading List
Elementary Differential Equations and Boundary Value Problems, Boyce
and DiPrima, Wiley (continuing students should already have a copy from year 2).

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  HDEq 
Contacts
Course organiser  Dr Tom MacKay
Tel: (0131 6)50 5058
Email: 
Course secretary  Miss Greta Mazelyte
Tel:
Email: 

